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1. A Comparative Study of Formulations and Algorithms for Reliability-Based Co-Design Problems

   https://doi.org/10.1115/DETC2019-98307  

   Cui, Tonghui ; Allison, James T. ; Wang, Pingfeng ( August 2019 , American Society of Mechanical Engineers)

   Co-design, or integrated physical and control system design, has been demonstrated successfully for several engineering system design optimization applications, primarily in a deterministic manner. An opportunity exists to study non-deterministic co-design strategies, including incorporation of uncertainty-induced failures, into an integrated co-design framework. Reliability-based design optimization (RBDO) is one such method that can be used to increase the likelihood of having a feasible design that satisfies all reliability constraints. While significant recent advancements have been made in co-design and RBDO separately, limited work has been done where reliability-based dynamic system design and control design optimization are considered jointly. In this paper, the co-design problem is integrated with the RBDO framework to yield a system-optimal design and the corresponding control trajectory, which satisfy all reliability constraints in the presence of parameter variations. Different problem formulations and RBDO algorithms are compared through numerical examples. The design of a horizontal-axis wind turbine (HAWT) supported by a lattice tower (with parameter uncertainties) is presented to demonstrate the applicability of the proposed method. 

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2. Control Barrier Functions for Complete and Incomplete Information Stochastic Systems

   https://doi.org/https://doi.org/10.23919/ACC.2019.8814901  

   Clark, A. ( January 2019 , American Control Conference (ACC))

   Real-time controllers must satisfy strict safety requirements. Recently, Control Barrier Functions (CBFs) have been proposed that guarantee safety by ensuring that a suitablydefined barrier function remains bounded for all time. The CBF method, however, has only been developed for deterministic systems and systems with worst-case disturbances and uncertainties. In this paper, we develop a CBF framework for safety of stochastic systems. We consider complete information systems, in which the controller has access to the exact system state, as well as incomplete information systems where the state must be reconstructed from noisy measurements. In the complete information case, we formulate a notion of barrier functions that leads to sufficient conditions for safety with probability 1. In the incomplete information case, we formulate barrier functions that take an estimate from an extended Kalman filter as input, and derive bounds on the probability of safety as a function of the asymptotic error in the filter. We show that, in both cases, the sufficient conditions for safety can be mapped to linear constraints on the control input at each time, enabling the development of tractable optimization-based controllers that guarantee safety, performance, and stability. Our approach is evaluated via simulation study on an adaptive cruise control case study. 

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3. An Overview of Uncertain Control Co-Design Formulations

   https://doi.org/10.1115/1.4062753  

   Azad, Saeed ; Herber, Daniel R. ( September 2023 , Journal of Mechanical Design)

   This article explores various uncertain control co-design (UCCD) problem formulations. While previous work offers formulations that are method-dependent and limited to only a handful of uncertainties (often from one discipline), effective application of UCCD to real-world dynamic systems requires a thorough understanding of uncertainties and how their impact can be captured. Since the first step is defining the UCCD problem of interest, this article aims at addressing some of the limitations of the current literature by identifying possible sources of uncertainties in a general UCCD context and then formalizing ways in which their impact is captured through problem formulation alone (without having to immediately resort to specific solution strategies). We first develop and then discuss a generalized UCCD formulation that can capture uncertainty representations presented in this article. Issues such as the treatment of the objective function, the challenge of the analysis-type equality constraints, and various formulations for inequality constraints are discussed. Then, more specialized problem formulations such as stochastic in expectation, stochastic chance-constrained, probabilistic robust, worst-case robust, fuzzy expected value, and possibilistic chance-constrained UCCD formulations are presented. Key concepts from these formulations, along with insights from closely-related fields, such as robust and stochastic control theory, are discussed, and future research directions are identified. 

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4. Robust Maximum Coverage Facility Location Problem with Drones Considering Uncertainties in Battery Availability and Consumption

   https://doi.org/10.1177/0361198120968094  

   Chauhan, Darshan R. ; Unnikrishnan, Avinash ; Figliozzi, Miguel ; Boyles, Stephen D. ( February 2021 , Transportation Research Record: Journal of the Transportation Research Board)

   null (Ed.)

   Given a set of a spatially distributed demand for a specific commodity, potential facility locations, and drones, an agency is tasked with locating a pre-specified number of facilities and assigning drones to them to serve the demand while respecting drone range constraints. The agency seeks to maximize the demand served while considering uncertainties in initial battery availability and battery consumption. The facilities have a limited supply of the commodity being distributed and also act as a launching site for drones. Drones undertake one-to-one trips (from located facility to demand location and back) until their available battery energy is exhausted. This paper extends the work done by Chauhan et al. and presents an integer linear programming formulation to maximize coverage using a robust optimization framework. The uncertainty in initial battery availability and battery consumption is modeled using a penalty-based approach and gamma robustness, respectively. A novel robust three-stage heuristic (R3SH) is developed which provides objective values which are within 7% of the average solution reported by MIP solver with a median reduction in computational time of 97% on average. Monte Carlo simulation based testing is performed to assess the value of adding robustness to the deterministic problem. The robust model provides higher and more reliable estimates of actual coverage under uncertainty. The average maximum coverage difference between the robust optimization solution and the deterministic solution is 8.1% across all scenarios. 

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5. Probabilistic Microgrid Energy Management with Interval Predictions

   https://doi.org/10.3390/en13123116  

   Cheng, Jiayu ; Duan, Dongliang ; Cheng, Xiang ; Yang, Liuqing ; Cui, Shuguang ( June 2020 , Energies)

   null (Ed.)

   In this paper, we consider a probabilistic microgrid dispatch problem where the predictions of the load and the Renewable Energy Source (RES) generation are given in the form of intervals. A hybrid method combining scenario-selected optimization and reserve strategy using the Model Predictive Control (MPC) framework is proposed. Specifically, first of all, an appropriate scenario is selected by the optimizer at each optimization stage, and then the optimal scheduling and reservation of system capacity are determined based on the selected scenario and possible variations in the future as provided by the predictors. In addition, a new reserve strategy is introduced to adaptively maintain system reliability and respond to variations in the hierarchical microgrid control. Simulations are conducted to compare our proposed method with the existing robust method and the deterministic dispatch with perfect information. Results show that our proposed method significantly improves the system efficiency while maintaining system reliability. 

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